Which statement about the function is true? The function is positive for all real values of x where x > –4. The function is negative for all real values of x where –6 –3. The function is negative for all real values of x where x < –2.

Answer:

25 degrees

Step-by-step explanation:

The two given angles are vertical, so we can set their measures equal to each other and then solve for x.

4x + 50 = 150

4x = 100

x = 25

Answer:

x = 25

Step-by-step explanation:

The angles are vertical angles, so their measures are equal.

4x + 50 = 150

4x = 100

x = 25

The average cost of weekly groceries is $124.50."  The statistical measurement are they most likely claiming is Mean

The correct option is (B)

The arithmetic mean of a given data is the sum of all observations divided by the number of observations.

For example, a cricketer's scores in five ODI matches are as follows: 12, 34, 45, 50, 24. To find his average score in a match, we calculate the arithmetic mean of data using the mean formula:

Mean = Sum of all observations/Number of observations

The value of the middlemost observation, obtained after arranging the data in ascending or descending order, is called the median of the data.

For example, consider the data: 4, 4, 6, 3, 2. Let's arrange this data in ascending order: 2, 3, 4, 4, 6. There are 5 observations. Thus, median = middle value i.e. 4.

The value which appears most often in the given data i.e. the observation with the highest frequency is called a mode of data.

As per the situation we have given average cost of groceries.

The mean is also the average sum of data divided by total number of data.

Hence, The statistical measurement is Mean.

Learn more about mean here:

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Answer:

21 + 12i

Step-by-step explanation:

Given

(3 - 4i)(1 + 5i) - (2 - i) ← expand the product of factors using FOIL

= 3 + 11i - 20i² - 2 + i ( note i² = - 1 )

= 3 + 11i + 20 - 2 + i ← collect like terms

= 21 + 12i

Answer:

The answer is

Step-by-step explanation:

(3-4i)(1+5i)-(2-i)

Expand the terms in the bracket first

That's

3 + 15i - 4i - 20i² - ( 2 - i)

Remove the bracket

3 + 15i - 4i - 20i² - 2 + i

Group like terms

- 20(-1) + 15i - 4i + i + 3 - 2

15i - 4i + i + 20 + 3 - 2

Simplify

We have the final answer as

Hope this helps you

Answer:

Option (B)

Step-by-step explanation:

There are two lines on the graph representing the system of equations.

First line passes through two points (-3, 1) and (-2, 3).

Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

                           = [tex]\frac{3-1}{-2+3}[/tex]

                       m = 2

Equation of the line passing through (x', y') and slope = m is,

y - y' = m(x - x')

Equation of the line passing through (-3, 1) and slope = 2 will be,

y - 1 = 2(x + 3)

y = 2x + 7 ----------(1)

Second line passes through (0, 1) and (-1, 4) and y-intercept 'b' of the line is 1.

Let the equation of this line is,

y = mx + b

Slope 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

               = [tex]\frac{4-1}{-1-0}[/tex]

               = -3

Here 'b' = 1

Therefore, equation of the line will be,

y = -3x + 1 ---------(2)

From equation (1) and (2),

2x + 7 = -3x + 1

5x = -6

x = [tex]-\frac{6}{5}[/tex]

x = [tex]-1\frac{1}{5}[/tex]

From equation (1),

y = 2x + 7

y = [tex]-\frac{12}{5}+7[/tex]

  = [tex]\frac{-12+35}{5}[/tex]

  = [tex]\frac{23}{5}[/tex]

  = [tex]4\frac{3}{5}[/tex]

Therefore, exact solution of the system of equations is [tex](-1\frac{1}{5},4\frac{3}{5})[/tex].

Option (B) will be the answer.

Answer:

B. (-1 1/5, 4 3/5)

Step-by-step explanation:

Answer:

If I'm correct she bought 5 pounds of coffee.

Step-by-step explanation:

$70 (gift card)

-$26.80 (remainder on g.c.)

= $43.20 ($ spent on money)

$43.20/ $8.64 = 5

(remainder)/ cost per lb. = lbs of coffee bought

Answer: She bought 5 pounds of coffee

Step-by-step explanation:

This situation can be represent by the equation

70 - 8.64 x = 26.80  where x is the number of coffee she bought.   solve for x

-70                   -70

-8.64x = -43.20

x = 5

Answer:

d. (4) + (-5)

Step-by-step explanation:

We know that 4 is the positive value and 5 is the negative value, therefore if to be able to rewrite in it we will almost make a sum of these values without changing the meaning of each one of the values, therefore:

(+4) + (-5)

Which means that the correct option is the last option, that is, d. (4) + (-5). Furthermore, the representation is correct because the resulting arrow is the one corresponding to -1.

Answer:

5 ≤ The number of packages Renna can remove

Step-by-step explanation:

The allowable mass on the elevator is given as 450 kg

The mass of Renna and the packages = 620 kg

The mass of each package = 37.4 kg

The mass Renna should remove from the elevator to meet the mass requirement = 620 - 450 = 170 kg

Therefore, the number of packages, n, Renna should remove can be found from the following inequality

170 ≤ n × 37.4

We note that since the mass of the packages are known, 5 packages weigh 187 kg which is > 170 kg

Therefore, the number of packages to be removed is 170 ≤ n × 37.4 < 187

Dividing by 37.4, we get;

Number of packages to be removed = 4.55 ≤ n < 5 ≈ 5 packages

Given that there whole number packages, we have;

5 ≤ n, which is , 5 ≤ The number of packages Renna can remove.

Answer:

37.4p  ≥ 170

Step-by-step explanation:

5 are in total packages.

Trust me this is the answer because I did this before

Hope this helps ;)

Answer:

The quadrilateral shown is a kite, because it has two non-congruent pairs of congruent sides

x = 3

Step-by-step explanation:

The vertex angles in a kite are bisected by the diagonals.  Thus, 11x = 9x + 6.

11x=9x+6

2x=6

x=3

Hope it helps <3

Answer:

Step-by-step explanation:

[tex]21\: square\:meters = 6 \:wizard \:cloak\\x\:square\:meters\:\:=4 \:wizard\:cloaks\\\\Cross\:Multiply\\6x = 84\\\frac{6x}{6} =\frac{84}{6} \\\\x = 14 \:square\:meters[/tex]

Answer:

14.0 square meters

Step-by-step explanation:

Answer:

x=7/10

Step-by-step explanation:

2/5=4/10

11/10=x+4/10

11/10-4/10=x

7/10=x

Answer:

x=7/10 or 0.7

Step-by-step explanation:

I turned the fractions into decimals

so

1.1=x+0.4

subtract 0.4 from 1.1 to get 0.7

Turn it into a fraction which is 7/10

Answer:

The ratio of the average change in profit when the level of production changes from 600 to 620 units per month is -24 : 5.

Step-by-step explanation:

The question is:

A company knows that if it produces "x" monthly units its utility "u" could be calculated with the expression: u (x) = - 0.04x ^ 2 + 44x-4000 where "u" is expressed in dollars. Determine the ratio of the average change in profit when the level of production changes from 600 to 620 units per month. Remember that the slope of the secant line to the graph of the function represents the average rate of change.

Solution:

The expression for the utility is:

[tex]u (x) = - 0.04x ^ {2} + 44x-4000[/tex]

It is provided that the slope of the secant line to the graph of the function represents the average rate of change.

Then the ratio of the average change in profit when the level of production changes is:

[tex]\text{Average change in profit}=\frac{u(x_{2})-u(x_{1})}{x_{2}-x_{1}}[/tex]

Compute the values of u (x₁) and u (x₂) as follows:

x₁ = 600

[tex]u (x_{1}) = - 0.04x_{1} ^ {2} + 44x_{1}-4000[/tex]

         [tex]= - 0.04(600) ^ {2} + 44(600)-4000\\=-14400+26400-4000\\=8000[/tex]

x₂ = 620

[tex]u (x_{2}) = - 0.04x_{2} ^ {2} + 44x_{2}-4000[/tex]

         [tex]= - 0.04(620) ^ {2} + 44(620)-4000\\=-15376+27280-4000\\=7904[/tex]

Compute the average rate of change as follows:

[tex]\text{Average change in profit}=\frac{u(x_{2})-u(x_{1})}{x_{2}-x_{1}}[/tex]

                                      [tex]=\frac{7904-800}{620-600}\\\\=\frac{-96}{20}\\\\=-\frac{24}{5}\\\\=-24:5[/tex]

Thus, the ratio of the average change in profit when the level of production changes from 600 to 620 units per month is -24 : 5.

Answer:

Step-by-step explanation:

From the given information:

the null and alternative hypotheses in symbolic form for this claim can be computed as:

[tex]H_o:\mu = 18 \\ \\ H_a : \mu > 18[/tex]

Mean = [tex]\dfrac{18.5+18.2+20+21.3+17.9+17.9+18.1+17.5+20+18}{10}[/tex]

Mean = 18.74

Standard deviation  [tex]\sigma = \sqrt{\dfrac{\sum(x_i - \mu)^2}{N}}[/tex]

Standard deviation  [tex]\sigma = \sqrt{\dfrac{(18.5 - 18.74)^2+(18.2 - 18.74)^2+(20 - 18.74)^2+...+(18 - 18.74)^2}{10}}[/tex]

Standard deviation [tex]\sigma[/tex]   = 1.18

The test statistics can be computed as follows:

[tex]Z= \dfrac{X- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z= \dfrac{18.6- 18}{\dfrac{1.18}{\sqrt{10}}}[/tex]

[tex]Z= \dfrac{0.6}{\dfrac{1.18}{3.162}}[/tex]

Z = 1.6078

Z = 1.61

Degree of freedom = n -1

Degree of freedom = 10 -1

Degree of freedom = 9

Using t - calculator at Z = 1.6078 and df = 9

The P - value = 0.0712

Answer:

D

Step-by-step explanation:

From the graph, the y-intercept of f(x) is 2 and since the y-intercept is when x = 0, it would fall into the x ≤ 1 category so the y-intercept of g(x) is 0 - 4 = -4. Since 2 > -4, the answer is D.

Answer:

5.76

Step-by-step explanation:

Answer:

$105

Step-by-step explanation:

Each student buys one package of seeds and one container

s = Amount of students; p = price of seed package; c = price of container

s*(p+c)=30(1.00+2.50)=30(3.5)$105.

Hope This Helps!

Answer:

0.638 seconds

Step-by-step explanation:

Since the ball is being dropped from a height of 24 meters, the equation will look like this:

24=9.8/s^2.

This is asking for how much seconds it will take for the ball to fall 24 meters to the ground.

Solve the equation:

24(s^2)=9.8

(s^2)=0.408

s^2=0.408

root the number:

0.638

you can round it to the nearest whatever it's asking you to round it to

Im not an expert, so please excuse me if it's not done correctly

Answer:

to be honest I'm not sure how to do

Answer: 5.24 units, 10.48 units , 15.72  units

Step-by-step explanation:

Volume of a rectangular solid is given by :-

V = lwh, where l = length , w= width and h = height

Given: A rectangular solid has edges whose lengths are in the ratio 1:2:3.

Let lengths of the rectangular solid x , 2 x, 3x.

volume of the solid is 864 cubic units

Then, Volume of rectangle = [tex]x (2x)(3x) =864\ \text{cubic units}[/tex]

[tex]\Rightarrow\ 6x^3 = 864\\\\\Rightarrow\ x^3 =144\\\\\Rightarrow\ x=(144)^{\frac{-1}{3}}\approx5.24[/tex]

Lengths of rectangular solid 5.24 units, 2 (5.24) units , 3(5.24) units

= 5.24 units, 10.48 units , 15.72  units

Answer:3.2 ft

Step-by-step explanation:

sin 32°=[tex]\frac{yz}{6}[/tex]

cross multiply

sin 32° x 6=yz

0.5299 x 6 =yz

yz=3.1795

≅3.2ft

Answer:

H

Step-by-step explanation:

here, the question says that the given regular hexagon needs to be rotated counter clockwise 300°, considering the edges labels, each movement from one edge to other is 60° as 360/6 =60.

focus on N and move on anti clockwise.

When N rotates anti clockwise about center from original to position G, is 60°,

when N moves on anti clockwise about center from original to position A is 120°.

similarly, to X is 180°, to E is 240° and to H is 300°.

so, the new position of N when rotated anti clockwise about origin of the hexagon will be at H.

Answer: The sum is 127

Step-by-step explanation:

A 2-digit number N = ab can be written as (where a and b are single-digit numbers)

a*10 + b.

Now, we want that:

(a + 2)*(b + 2) = a*10 + b.

So we must find all the solutions to that equation such that a can not be zero (if a = 0, then the number is not a 2-digit number)

We have:

(a + 2)*(b + 2) = a*b + 2*a + 2*b + 4 = a*10 + b

a*b + 2*b - b + 4 = a*10 - a*2

a*b + 4 + b = a*8

a*b + 4 + b - a*8 = 0.

Now we can give one of the variables different values, and see if the equation has solutions:

>a = 1:

1*b + 4 + b - 8 = 0

2*b - 4 = 0

b = 4/2 = 2

Then the number 12 has the property.

> if a = 2:

2*b + 4 + b -16 = 0

3b -12 = 0

b = 12/3 = 4

The number 24 has the property.

>a = 3 is already known, here the solution is 35.

>a = 4.

4*b + 4 + b - 8*4 = 0

5*b + 4 - 32 = 0

5*b = 28

b = 28/5

this is not an integer, so here we do not have a solution.

>if a = 5.

5*b + 4 + b - 8*5 = 0

6b + 4 - 40 = 0

6b - 36 = 0

b = 36/6 = 6

So the number 56 also has the property.

>if a = 6

6*b + 4 + b - 8*6 = 0

7b + 4 - 48 = 0

7b - 44 = 0

b = 44/7 this is not an integer, so here we do not have any solution.

>if a = 7

7*b + 4 + b -8*7 = 0

8b -52 = 0

b = 52/8 = 6.5 this is not an integer, so we here do not have a solution.

>if a = 8

8*b + 4 + b -8*8 = 0

9*b + 4 - 64 = 0

9*b = 60

b = 60/9 this is not an integer, so we here do not have any solution:

>if a = 9

9*b + 4 + b - 8*9 = 0

10b + 4 - 72 = 0

10b -68 = 0

b = 68/10 again, this is not an integer.

So the numbers with the property are:

12, 24, 35 and 56

And the sum is:

12 + 24 + 35 + 56 =  127

Answer:

Step-by-step explanation:

The given set of data is 83, 71, 62, 86, 90, 95, 61, 60, 87, 72, 95, 74, 82, 54, 99, 62, 78, 76, 84, 92.

Now the stem - leaf plot will be,

5  4

6  0   1   2   2

7   1   2  4   6    8

8 2   3  4   6    7

9  0   2  5   5   9

Since range of the data = Highest term of the data - Lowest term of the data

                                       = 99 - 54

                                       = 45

Therefore, range of the data set is 45.

The range of the data is 45.

As we know that

Since range of the data = Highest term of the data - Lowest term of the data

= 99 - 54

= 45

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Answer:

Step-by-step explanation:

The length of side length VY is 4z+2

The same as side length WX

Answer:

The original width was 94.71 cm

Step-by-step explanation:

Given:

new smaller area = 1.2m^2

Decrease in length of the rectangular sheet = 34.5cm

Therefore:

1. the final width of the sheet is given as

2X^2 = 1.2 m^2

X^2 - 0.6 m^2

X^2 = 10000 * 0.6 cm

X = 77.46 cm (this is the width)

2. The length of the sheet

= 2 * 77.46

= 154.92 cm.

3. Initial length of the sheet

= 154.92 + 34.5

= 189.42 cm.

4. Initial width of the sheet ( original ).

= 189.42 / 2

= 94.71 cm.

5. Initial area of the sheet

= 94.71 * 189.92

= 17939.9 cm^2

New area of the sheet

= 79.46 * 154.92

= 12000.1 cm^2

Difference between the initial and new area

= 17939.9 - 12000.1

= 5939.86 cm^2

Percentage of area decrease

= 5939.86 ' 17939.9

= 33.1%

Step-by-step explanation:

the first answer is 72 as it is it

Answer:

The answer is 8.

Step-by-step explanation:

The product of 12 and 3 is 36. One-fourth of 36 is 9. 5 subtracted from 9 is 4.

Answer:

x = 2

Step-by-step explanation:

Add 5 to both sides to get the 5 to the right side since we are trying to isolate the variable x:

3x – 5 + 5 = 1 + 5

Simplify: 3x=6

Divide each side by 3 to isolate and solve for x:

3x/3=6/3

Simplify: x=2

Answer:

  B(-6, 0)

Step-by-step explanation:

You want to find B such that ...

  (B -A) = (3/4)(C -A) . . . . the required distance relation

  4(B -A) = 3(C -A) . . . . . . multiply by 4

  4B = 3C +A . . . . . . . . . . add 4A, simplify

Now, we can solve for B and substitute the given coordinates:

  B = (3C +A)/4 = (3(-6, -2) +(-6, 6))/4 = (-24, 0)/4 = (-6, 0)

The coordinates of point B are (-6, 0).

Answer:

the answer your looking for is (-3,-3)

Step-by-step explanation:

Answer:

301.59

Step-by-step explanation:

your answer was almost right you just forgot to multiply by 9

Answer:

(6, 1)

Step-by-step explanation:

x + 2y = 8

1. subtract 2y to get x alone -- x = -2y + 8

2. insert (-2y + 8) as x

2x - 2 = 10

2(-2y + 8) -2 = 10

3. distribute the 2

-4y + 16 - 2 = 10

4. combine like terms

-4y + 14 = 10

5. subtract 14 from both sides

-4y = -4

6. divide by -4

y = 1

7. plug y into any of the two original equations

x + 2(1) = 8

8. simplify

x + 2 = 8

x = 6

9. check answer with second equation

2(6) - 2 = 10

12 - 2 = 10

Answer:

152.87 degree/seconds

Step-by-step explanation:

1 rotation = Circumference of a circle = 2πr

r = 15 inches

1 rotation = 2 × 3.14 × 15

94.2 inches.

We are told in the question that it takes 30 seconds to roll 100 feet along the ground

Convert feet to inches

1 feet = 12 inches

100 feet =

100 × 12 = 1200 inches.

Hence, if

94.2 inches = 1 rotation

1200 inches = X

Cross multiply

94.2 × X = 1200 × 1

94.2X = 1200

X = 1200/94.2

X = 12.738853503 rotations

Formula for Angular velocity = Number of rotations × 2π/time in seconds

Time = 30 seconds

12.738853503 × 2 × 3.14/30

= 2.6666666667 rotations per second

Converting Angular velocity to degree per second

= 2.6666666667 × 180/ π

= 2.6666666667 × 180/3.14

= 152.86624204 degree/seconds

Approximately to 2 decimal places

= 152.87 degree/seconds

Answer:

A. Undefined slope (no slope)

B. [tex]\frac{5}{4}[/tex]

Step-by-step explanation:

A slope is rise over run.

The points (6, 2) and (6, -3) are located on the same x coordinate, therefore they have an undefined slope.

However, the points (-4, -7) and (4, 3) do have a slope. The rise is 10 ( | -7+ 3 | ) and the run is 8 ( | -4 + 4 | ). 10/8 is equivalent to 5/4.

Hope this helped!